Range-dependent regularization of travel-time tomography based on theoretical modes

Travel time inversion is a fundamental method of Ocean Acoustic Tomography, for the estimation of perturbations in sound speed. By discretizing the watercolumn into a system of layers, the method allows to introduce a system of linear equations, relating a known vector of perturbations in travel time, to an unknown vector of perturbations in sound speed, through the so-called \observation matrix". Inverting the system allows to determine a solution, which estimates the perturbation in sound speed in each layer of the watercolumn. However, in most problems of practical interest, the number of unknowns (i.e. the perturbations in sound speed) is larger that the number of equations (which correspond to the number of delays in travel time), which implies that inverting the system of linear equations can be viewed as an ill-posed problem. The discussion presented in this paper illustrates an approach to the problem of inversion, which is based on the usage of theoretical modes. Further, it is shown that for a range-dependent perturbation in sound speed, which corresponds to a superposition of plane waves, the inversion problem can be regularized (i.e. the system of linear equations can be rewritten in order to deal with more equations than unknowns) by estimating only the amplitudes and phases of the linear waves. Particular examples are given for simulated and real data